The Coast Guard as established January 28, 1915, shall be a military service and a branch of the armed forces of the United States at all times. The Coast Guard shall be a service in the Department of Homeland Security, except when operating as a service in the Navy.

Khun Joe misunderstands the categories he’s quoting. Members of the Armed Forces are military, whether they’re serving in one of the Military Departments or not. Hopefully this Venn diagram will help:
I won’t use the IANAL disclaimer; I’m an alumnus of both the U.S. Coast Guard Academy and the CWRU School of Law. Hope this helps, Joe!